A Test of the Conditional Independence Assumption in Sample Selection Models

Abstract

Summary Identification in most sample selection models depends on the independence of the regressors and the error terms conditional on the selection probability. All quantile and mean functions are parallel in these models; this implies that quantile estimators cannot reveal any—per assumption non‐existing—heterogeneity. Quantile estimators are nevertheless useful for testing the conditional independence assumption because they are consistent under the null hypothesis. We propose tests of the Kolmogorov–Smirnov type based on the conditional quantile regression process. Monte Carlo simulations show that their size is satisfactory and their power sufficient to detect deviations under plausible data‐generating processes. We apply our procedures to female wage data from the 2011 Current Population Survey and show that homogeneity is clearly rejected. Copyright © 2015 John Wiley & Sons, Ltd.

Unobserved selection heterogeneity and the gender wage gap

“…Identification under the control function approach requires an exclusion restriction, 5 that is, an instrument Z that shifts employment but is unrelated to wages. Also, Huber and Melly (2015) cast doubt on the validity of traditional sample selection models in female wage regressions and, in particular, on the empirical findings in Mulligan and Rubinstein, as they imply that all explanatory variables are restricted to have the same effect at different quantiles of the outcome distribution. In particular, Bar et al (2015) show that a generalized version of the standard selection model uncovers a much smaller role of selection bias than what was documented by Mulligan and Rubinstein (2008).…”

“…In contrast to a parametric selection correction, the bounding approach relying on an instrument imposes fewer restrictions as it need not model selection. This paper is mostly related to the approaches that allow selection to depend on unobservables and rely on an exclusion restriction, such as the approaches in Mulligan and Rubinstein (2008), Bar et al (2015), Blundell et al (2007), Huber and Melly (2015), and Arellano and Bonhomme (2017). In Blundell et al (2007), the availability of an instrument 6 is combined with a positive selection assumption and an additivity restriction in the wage equation for an empirical assessment of the gender wage gap in the UK.…”

The Residency Discount for Rents in Germany and the Tenancy Law Reform Act 2001: Evidence from Quantile Regressions

“…9 Using data of 102 apartment complexes in US-American metropolitan areas, Barker (2003) finds that discounts for short-term tenants are more common. First, how to account for selection when estimating quantile regression is still subject of an intensive debate (Huber and Melly, 2012). Sims (2007) analyzes the effect of rent control in various cities in Massachusetts that ended in 1995.…”

Robust Inference in Sample Selection Models

“…Moreover, when an exclusion restriction is available, we add the quantile regression estimator. This is the estimator that was proposed by Buchinsky () and extended by Huber and Melly (), which is a combination of a semiparametric binary regression as in Klein and Spady () in the first stage and quantile regression in the second stage. It is computed by using the code kindly provided to us by M. Huber.…”

“…() in the statistical literature and Peracchi (, ) and Ronchetti and Trojani () in the econometric literature. In particular, the quantile regression approach (Koenker, ) has proved fruitful as a specific way to robustify classical procedures and, in the framework of sample selection models, it has been proposed by Buchinsky () and Huber and Melly (). Details about this approach are provided in Section .…”